D74/2010 - On a Asymptotic Behaviour of the Solution for a Stochastic Coupled System of Reaction-Difusion of Nonlocal Type

Preprint D74/2010

On a Asymptotic Behaviour of the Solution for a Stochastic Coupled System of Reaction-Difusion of Nonlocal Type

Paulo Magalhães | Ferreira, Jorge | Coayla-Teran, Edson

Keywords: Multiplicative white noise. Stochastic coupled system of reaction-difusion. Asymptotic behaviour. Existence and uniqueness.

In this article we investigate the existence and uniqueness of the strong solutions for a stochastic nonlinear parabolic coupled system of reaction-difusion of nonlocal type with multiplicative white noise. We improve the results obtained by Coayla-Ferreira-Magalhães for coupled systems. We prove the existence and uniqueness of strong solutions by the classic Faedo-Galerkin method, Itô formula and some technical ideas. An important result on the asymptotic behaviour of solution is presented.